Continuous Wave Coherent
Lyman-alpha

As explained in 'Antihydrogen
spectroscopy', light at 121.56 nm (Lyman-alpha) is necessary to do
laser cooling on antihydrogen. Unfortunately, Lyman-alpha is a bit of a
nasty wavelength. It is part of the vacuum ultraviolet (VUV) wavelength
region between 100 nm and 200 nm where most materials are opaque. Light
in this wavelength region is immediately absorbed by air. Therefore we
have to guide the light in vacuum or buffer gasses such as helium or argon.
The only two materials with an appreciable transmission for Lyman-alpha
are magnesium fluorite (MgF2) and lithium fluorite (LiF) crystals. In practical
terms MgF2 is the best, but every lens of a few mm thickness absorbs already
50 %!. Also any occurrence of water or other substances strongly reduce
Lyman-alpha intensity. This is why it is such a difficult wavelength to
work with.

The most simple source of Lyman-alpha is a hydrogen lamp.
However, the broad spectrum of these lamps (~ 30 GHz) render them fairly
useless for laser cooling. So far the best sources of narrow bandwidth
Lyman-alpha have been based on high power pulsed lasers and non-linear
optical processes. With such a source laser cooling to 8 mK of magnetically
trapped hydrogen has been successfully demonstrated in Amsterdam [1]. The
most ideal source of Lyman-alpha would have the following characteristics:

Such a continuous source would open several new possibilities.
For one thing, it should be able to reach the cooling Doppler limit of
~ 3mK. Also, the narrow bandwidth results in an excellent state selectivity
such that the chance of exciting the wrong (not-trapped) magnetic sublevels
is minimized. When powerful enough (at least 1012 photons/s),
Zeeman-slowing antihydrogen into a magnetic trap becomes feasible.
Another possibility is using 1S-2P transition fluorescence to detect a
1S-2S transition events. This can be done by 'shelving spectroscopy':
if the atom is in the 2S, it cannot scatter Lyman-alpha anymore. A transition
1S-2S is then detectable by looking for Lyman-alpha fluorescence dips.

With these advantages in mind we have developed
the first continuous, coherent, Lyman-alpha source in the world [2].
Our source is based on four-wave-mixing. In this process three different
laser beams are focused in the same volume of a mercury vapor oven.
Due to the high intensity laser beams, the electrons in mercury start to
oscillate in a anharmonic way. As a result a little bit of light is generated
at the sum frequency of the three incoming laser beams:

To appreciate the difficulty of generating continuous
wave Lyman-alpha, one has to realize that the yield of the four-wave-mixing
process depends heavily on the power of the incoming laser beams:

Output power VUV
= N2 * X2(3) * F * P1*P2*P3

where N=mercury density, X(3)=third order non-linear
susceptibility, F=phasematching integral, and P1*P2*P3
is the product of the three input laser powers. Pulsed lasers have a peak
power generally 7 orders of magnitude higher than that of typical continuous
lasers. As a result it is far more easy to do pulsed four-wave-mixing as
the factor P1*P2*P3 is more than 20 orders
of magnitude larger!

Fortunately two aspects work in favor of four-wave-mixing
with continuous instead of pulsed lasers (with typically ns long pulses):

one can go closer to the atomic resonances without immediately
ionizing the atom.

By choosing the wavelength close to
resonances in the atom, one can increase the response of the electrons
in mercury on the light by many orders of magnitude. The picture to the
left shows a simplified energy diagram of mercury, and the different colors
we use to generate Lyman-alpha light. Especially the exact two-photon resonance
is vital to improve the efficiency of the process. Further yield improvement
is accomplished by the near 1- and 3-photon resonances.

As a result continuous four-wave-mixing can still generate
an appreciable amount of light. From ~ 500 mW at 257 nm, 700 mW at 399
nm, and 1.4 W at 545 nm, we have generated so far almost 1010
photons/s (~10nW) at 121.56 nm. It is already one of the stronger Lyman-alpha
sources that have been built, and the only continuous coherent one. The
energy conversion efficiency is 0.5*10-8. If light bulbs would
be as inefficient as this we would need a bulb of 600 000 000 W to have
the same amount of light as a standard 60W bulb generates! The highest
yield we reached at 122 nm with almost 200 nW.

Although 10 nW at Lyman-alpha may not sound much, it is
already enough to do effective laser cooling of antihydrogen.